V-shaped grooves that by two ray bounces emulate the functionality of a single-bounce reflector of light have been proposed and used in different applications. For instance, grooves with flat facets and cylindrical symmetry on a flat surface are known as a brightness-enhancing film (BEF), manufactured by the 3M Corporation under the brand name Vikuiti, for displays.
The same geometry but used in a different way (as a reflector of solar beam radiation) was proposed to make heliostats for solar thermal energy by M. O'Neill, “Analytical and Experimental Study of Total Internal Reflection Prismatic Panels for Solar Energy Concentrators” Technical Report No. D50000/TR 76-06, E-Systems, Inc., P.O. Box 6118, Dallas, Tex. (1976), and A. Rabl, “Prisms with total internal reflection,” Solar Energy 19, 555-565 (1977), also U.S. Pat. No. 4,120,565 By A. Rabl and V. Rabl.
A parabolic dish reflector using V-shaped radial grooves on the paraboloid surface (i.e., the guiding lines of the grooves are contained in meridian planes of the original parabolic reflector) is being manufactured by the company Spectrus (http://www.spectrusinc.com/) for illumination applications. See, for instance, the “Reflexor Retrofit system” at http://spectrusinc.com/products-detail/reflexor-retrofit-system-178/8/. Similar reflectors were also proposed for solar applications. See A. Rabl, Prisms with total internal reflection, Solar Energy 19, 555-565 (1977) and also U.S. Pat. No. 4,120,565 to A. Rabl and V. Rabl. See also M. O'Neill, Analytical and Experimental Study of Total Internal Reflection Prismatic Panels for Solar Energy Concentrators, Technical Report No. D50000/TR 76-06, E-Systems, Inc., P.O. Box 6118, Dallas, Tex. (1976). In those designs, the cross section of the grooves is flat, which limits the device performance unless the groove size is small compared to the receiver or source sizes.
Improving that groove-size limitation, patent application US 2008/0165437 A1 by DiDomenico discloses a design method for V-shaped radial grooves the cross-sectional profile of which is not flat, and applies that method to parabolic dish reflectors. The non-flat profile is designed by parameterizing the surface using Bezier splines and using a numerical multi-parameter optimization method to minimize a certain cost function. The convergence of such a method to a global minimum is not guaranteed, and paragraph [0110], page 10 of US 2008/0165437 A1 specifically mentions the existence of many local minima that may trap the optimization algorithm, and explains that the selection of the cost function and the initial guess of the free-form surfaces are “critical.” No example of that cost function is given in US 2008/0165437 A1.
US 2008/0165437 A1 also discloses other devices as the XX (two reflecting surfaces) or RXI whose V-shaped radial grooves are designed by such an optimization procedure. No description is given of how the non-grooved surfaces are designed. US 2008/0165437 A1 claims in paragraph [0177], page 36 that their devices perform close to the physical limits. However, two contradictions are visible:
1. In FIG. 6A of US 2008/0165437 A1, the edge rays at the input are clearly not transformed into edge rays at the output, which is the necessary and sufficient condition to achieve the claimed physical limit (maximum concentration). The edge rays at the input are those contained in the surface of the cones (labeled as 305 in FIG. 3 and named so in paragraph [0146], page 33 of US 2008/0165437 A1), and the rays at the output must impinge on the contour of circle 610 of said FIG. 6A. The fact the input rays are well inside the circle 610 indicates that the phase space volume is far from been fully filled, and thus it performs also far from the concentration limit.
2. The device shown in FIG. 15B of US 2008/0165437 A1 cannot be a well performing concentrator device, since its thickness at the center is only 0.19 times the diameter, which is below the compactness limit of that concentrator device (0.23) easily deducible from the Fermat principle.
Summarizing, the grooved reflectors in the prior art are limited to guiding lines which are either straight parallel lines (i.e. prismatic 90° retroreflectors) or radial planar curves, and the cross section profile of the groove is flat or Bezier splines optimized by numerical algorithms.